Currently, there is significant interest in narrow-band bandstop, or notch, filters for use in advanced communication systems. A notch filter is used in the signal path of a receiver or transmitter to suppress undesired signals in a narrow band of frequencies, signals that would otherwise compromise system performance. For example, notch filters can be used to remove interference from receiver front-ends due to collocated transmitters, adjacent receive bands, and jammers, and can be used in transmitters to eliminate harmonic and spurious signals due to power amplifier nonlinearities.
Any means of attenuating electromagnetic power over a limited frequency band or bands is typically called a bandstop, band-reject, or notch filter. Conventional notch filter performance, as measured by stopband attenuation, passband insertion loss, and selectivity—which is the ratio of stopband width, bs, to the width between passband edges, bp—is ultimately limited by the “unloaded quality factor”, unloaded Q or Qu, of the resonators that comprise the filter. Since Qu is generally proportional to resonator volume and cost, the quest for a more effective notch filter (one with greater stopband attenuation, lower passband loss, and greater selectivity) is at odds with the perpetual drive towards miniaturization and cost reduction.
It is conventional practice to construct notch filters from resonant elements, or resonators, that behave as either shunt low impedances or series high impedances at their resonant frequencies such that they reflect incident power, and thereby attenuate the transmission of incident power, at these frequencies. For instance, a common way to attenuate the power through a transmission line at a particular microwave frequency is to couple a resonant element to the transmission line, as shown in FIG. 1, wherein both the power dissipation (or loss, which is typically quantified by the inversely related Qu) of the resonance and the level of the coupling between the resonance and the transmission line determine the attenuation Lo at the resonant frequency fo as well as determine the frequency span b about fo outside of which a certain maximum level of insertion loss is not exceeded. Examples of such a traditional bandstop filter would include an open-circuited half-wavelength microstrip transmission line resonator capacitively (gap-) coupled to a microstrip transmission line, as well as a TE01-mode dielectric-resonator-loaded cavity inductively (loop-) coupled to a coaxial transmission line.
Unfortunately, in these types of bandstop filters, the relative bandwidth
  b  =                                  f          1          2                -                  f          o          2                                      f          1                ⁢                  f          o                        for an attenuation L1 at a frequency f1 is dependent on both the maximum attenuation Lo at resonant frequency fo and the resonator's quality Qu, according to:
                    b        =                              1                          Q              u                                ⁢                                                                      10                                                            L                      o                                        /                    10                                                  -                                  10                                                            L                      1                                        /                    10                                                                                                10                                                            L                      1                                        /                    10                                                  -                1                                                                        (        1        )            When attenuation level L1=10 log10(2)≈3 dB, b is called the relative 3 dB bandwidth b3dB, and:
                              b                      3            ⁢                                                  ⁢            dB                          =                              1                          Q              u                                ⁢                                                    10                                                      L                    o                                    /                  10                                            -              2                                                          (        2        )            Consequently, for a fixed Qu, the greater the maximum attenuation is, the larger the relative bandwidth, while the narrower the relative bandwidth is, the less the maximum attenuation. Also, for a fixed level of coupling between the resonance and the transmission line, the maximum attenuation is dependent on the resonator Qu, so that a resonance with a lower Qu results in a wider relative bandwidth, smaller maximum attenuation, and lower filter selectivity. To emphasize the drawbacks of conventional notch filters, FIG. 2(a) illustrates the effect of Qu on Lo when b and resonator-to-transmission-line coupling are held constant, while FIG. 2(b) shows the effect of Qu on b when Lo and resonator-to-transmission-line coupling are held constant.
The only means of realizing better performance from optimally designed conventional notch filters is to employ resonators with commensurately higher Qu, which means either using relatively large waveguide cavity resonators, significantly smaller, but heavy and moderately expensive, single-mode or dual-mode dielectric resonators, or very expensive superconducting resonators that require cryogenic packaging and a cryocooler. Using higher Qu resonators unavoidably requires accepting some combination of a larger volume, a heavier weight, and a greater cost, as well as inherent incompatibility with conventional printed-circuit and integrated-circuit manufacturing processes.
U.S. Pat. No. 2,035,258, Hendrik W. Bode, issued Mar. 24, 1936, describes a lumped-element notch filter, shown in FIG. 3a, in which a series resonant circuit is connected in parallel with a shunt resonant circuit such that at a certain frequency the effective resistance and reactance of the two circuits are “simultaneously balanced,” resulting in “substantially infinite attenuation . . . at the frequency of balance.” FIG. 3b is a graph illustrating a representative transmission response of the filter of FIG. 3a. It is advantageous that the ultimate attenuation is substantially infinite and independent of the Qu of the reactive components comprising the resonant circuits. A disadvantage, however, is that the values of the constituent lumped inductors and capacitors must be exceptionally precise and that the ratios of the inductor values and the capacitor values in the circuits are impractically large. Consequently, it has not found wide use, especially at microwave frequencies where realizing lumped inductors is problematic.
U.S. Pat. No. 3,142,028, R. D. Wanselow, describes an alternate type of distributed-element microwave notch filter in which the reflection coefficient is independent of the amount of prescribed attenuation. The filter comprises a four-port, 3 dB, 90° hybrid (i.e., “quadrature”) waveguide coupler (also called a “3 dB short-slot forward wave directional coupler”) in which the two intermediate ports are each coupled to a separate, lossy-dielectric-filled cavity resonator. Both resonators have the same resonant frequency, and their Qu and coupling to the hybrid can be adjusted to realize a specific notch attenuation and bandwidth, with the resonators absorbing, rather than reflecting, incident power at their resonant frequencies. To reduce the size of Wanselow's filter, his circuit has subsequently been implemented using surface acoustic wave resonators and either a transmission line quadrature coupler or a lumped-element quadrature hybrid, as well as using a dual-mode dielectric resonator and a microstrip directional coupler.
U.S. Pat. No. 4,262,269 describes an approach that employs positive feedback around an amplifier and through a passive resonator to cancel the power dissipation in the resonator and effectively create an infinite-Qu active resonator. As in the '258 patent's filter, notch filters employing such active resonators exhibit an ultimate attenuation that is substantially infinite and independent of the Qu of the passive resonators. The approach, however, suffers from instability (a tendency to oscillate) inherent to positive feedback schemes, and while the approach significantly improves the stopband attenuation, it fails to improve, and can actually degrade, the band-edge noise figure.
U.S. Pat. No. 5,339,057 describes an alternate type of distributed-element active bandstop filter that employs inherently stable feedforward, rather than unstable positive feedback. Input power is channelized, or split, between an amplified unidirectional bandpass signal path and an amplified unidirectional delay signal path, as shown in FIG. 4a. An incident signal is split into two separate components, which are adjusted to be of equal amplitude and opposite phase at the desired frequency, and the adjusted components are recombined to form a notched output signal, with the stopband attenuation attributed to signal cancellation. FIG. 4b is a graph illustrating a representative transmission response of the filter of FIG. 4a. Although the maximum attenuation is independent of the resonator Qu and the invention introduces distributed transmission line elements, it requires an amplifier in the delay signal path. The noise, gain nonlinearities, and signal distortion inherent in any such amplifier in an all-pass signal path makes the invention generally unsuitable for many important applications, including receiver pre-select filtering and transmitter clean-up filtering.
U.S. Pat. No. 5,781,084, J. D. Rhodes, incorporated herein by reference, describes a fully passive non-reciprocal absorptive notch filter that exhibits a maximum attenuation independent of the constituent resonator Qu. The filter is composed of a three-port circulator, one port of which is terminated by a reflective single-port filter. When the reflective one-port filter is comprised of a single resonant circuit and the coupling between the resonant circuit and the circulator is adjusted so that, at resonance, the impedance of the resonant circuit is matched to the impedance of the circulator, then at resonance all the power supplied at the input port of the circulator is absorbed in the resistive part of the resonator, no power is transmitted to the output port of the circulator, and the notch filter exhibits infinite attenuation at the resonant frequency. The relative 3 dB bandwidth of Rhode's filter is expressed as:
                              b                      3            ⁢                                                  ⁢            dB                          =                  2                      Q            u                                              (        3        )            which, when compared with (2), makes it clear that both the relative bandwidth and resonator Qu are independent of the maximum notch attenuation, and visa versa. The filter also has the significant advantage that higher-order bandstop filter responses can be realized by simply terminating a circulator port with higher-order reflective one-port passive networks, so that only a single circulator is required for any order filter and the number of resonators is the same as the order of the bandstop filter response. This is in contrast to the active approaches discussed above, which require cascading of n first-order notch filters, including their respective amplifiers, to realize an nth-order bandstop filter response. Unfortunately, circulators are generally connectorized components, and although they can be made compatible with hybrid circuit manufacturing, they are generally much larger than semiconductor amplifiers and are incompatible with conventional monolithic printed-substrate and integrated circuit processing.
Another prior art channelized notch filter employs two active bandpass filter signal paths to realize directional-filter coupling (rather than simple directional coupling) to the delay signal path, using the principal of signal cancellation. Although this provides a low-distortion, amplifier-free “delay” signal path, it requires twice as many amplifiers and resonators, and three times the transmission line length and its associated insertion loss in the delay path.
There is, therefore, a need for an improved low-distortion narrow-band notch filter for which maximum attenuation is independent of resonator Qu, thereby effectively improving resonator Qu.
Miniature, electrically tunable bandstop filters are also needed for suppression of signal interference in the receivers, and suppression of spurious signal output from the transmitters, of frequency-agile and/or reconfigurable communication and sensor systems. Conventional tunable bandstop filters suffer appreciable performance variation and degradation over their frequency tuning range due to frequency dependent loss in the tuning elements and resonators, as well as frequency dependent coupling magnitude and frequency dependent phase shift in the coupling elements.
There is, therefore, also a need for an improved electrically tunable, low-distortion, narrow-band notch filter for which maximum attenuation is independent of resonator Qu and which substantially maintain their performance characteristics over their frequency tuning range.